Octagonal Prism

A prism is a solid in which two congruent and parallel polygons from the top and the bottom faces. Prism are often distinguished by the shape of their base polygon. The octagonal prism is formed by square sides and two regular octagon bases. If all faces of octagonal prism are regular, it is a semiregular polyhedron.

Below you could see some examples of octagonal prism:Example 1:The volume of an octagonal prism is 495 cubic millimeters. If the area of the base is 45 square millimeters, what is the height of the prism.

Volume of octagonal prism = AhWhere, A is the area of base and h be the height of a prism.

=> 495 = 45 x hStep 3:Solve for h,Divide both side by 45

=> $\frac{495}{45} = \frac{45 h }{45}$

=> 11 = h

or h = 11

Hence the height of the octagonal prism is 11 millimeter.Example 2 :What is the volume and surface area of the 10 ft high regular octagonal prism whose each side 5 ft and area of base is 65 square ft.Solution:Step 1:Area of base of the prism = 65 square ftHeight of the prism = 10 ftSide of base = 5 ftStep 2:Volume of octagonal prism = AhWhere, A is the area of base and h be the height of a prism.

=> V = 65 x 10

= 650

=> Volume pf the prism = 650 cubic ft.

Step 3:Surface area of the prism = 2A + 8ah

A = area of octagonal prism, a = side length of base and h = height of octagonal prism.